Criticism of Starmer has grown since details of the process to appoint Mandelson emerged last week.
Peter Mandelson had close contacts with the now-deceased American businessman Jeffrey Epstein, who was convicted of sex crimes.
Calls for resignation
Demands have been made for the Prime Minister's resignation and he is accused, among other things, of having misled parliament when he previously stated that procedures had been followed in Mandelson's appointment.
In a speech in the Houses of Parliament, Starmer discussed the vetting process for a prospective ambassador and said he had not been informed about the background check.
Starmer said he took full responsibility for the decision and apologised to the victims of Epstein's crimes.
"We have now changed the decision-making process," Starmer said in parliament, where members' reactions were repeatedly heard.
Missing information
The Prime Minister has claimed that he was not informed that Mandelson's security clearance had not been approved.
Mandelson had to step down when his close contacts with Epstein were revealed last year.
Since then, British Cabinet Secretary Chris Wormald has left his post, as have Downing Street's communications director Tim Allan and chief of staff Morgan McSweeney.
Conservative opposition leader Kemi Badenoch spoke after Starmer and said she believes the issue concerns Britain's national security.
